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Simplifying
(3x + 4z)(3x + -4z) = 0
Multiply (3x + 4z) * (3x + -4z)
(3x * (3x + -4z) + 4z * (3x + -4z)) = 0
((3x * 3x + -4z * 3x) + 4z * (3x + -4z)) = 0
Reorder the terms:
((-12xz + 9x2) + 4z * (3x + -4z)) = 0
((-12xz + 9x2) + 4z * (3x + -4z)) = 0
(-12xz + 9x2 + (3x * 4z + -4z * 4z)) = 0
(-12xz + 9x2 + (12xz + -16z2)) = 0
Reorder the terms:
(-12xz + 12xz + 9x2 + -16z2) = 0
Combine like terms: -12xz + 12xz = 0
(0 + 9x2 + -16z2) = 0
(9x2 + -16z2) = 0
Solving
9x2 + -16z2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '16z2' to each side of the equation.
9x2 + -16z2 + 16z2 = 0 + 16z2
Combine like terms: -16z2 + 16z2 = 0
9x2 + 0 = 0 + 16z2
9x2 = 0 + 16z2
Remove the zero:
9x2 = 16z2
Divide each side by '9'.
x2 = 1.777777778z2
Simplifying
x2 = 1.777777778z2
Take the square root of each side:
x = {-1.333333333z, 1.333333333z}
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